ABSTRACT In this work, we analyze the – model within the anisotropic electromagnetic–gravitational Hořava–Lifshitz theory. Starting from the Hamiltonian formulation of the electromagnetic–gravitational–dilaton system in dimensions obtained through a Kaluza–Klein reduction of the Hořava–Lifshitz theory, we consider the infrared regime with coupling constants , , and the dilaton fixed at its ground state . We show that the Hamiltonian can be written as the Einstein–Maxwell Hamiltonian plus a term proportional to the square of the trace of the canonical momentum . The preservation in time of the Hamiltonian constraint leads to an elliptic equation whose only asymptotically flat solution is , so the Hamiltonian reduces to the Einstein–Maxwell one on the constraint surface . We further analyze the constraint structure and show that the theory propagates four configuration–space physical degrees of freedom, corresponding to the two transverse–traceless gravitational modes and the two transverse electromagnetic modes of Einstein–Maxwell theory. We also show that the condition has a geometrical interpretation as the maximal slicing condition. Under asymptotically flat conditions and without additional boundary constraints, the anisotropic electromagnetic–gravitational Hořava–Lifshitz theory therefore becomes canonically equivalent to Einstein–Maxwell theory in maximal slicing. Consequently, gravitational and electromagnetic waves far from their sources propagate in exactly the same way in both theories.

ABSTRACT We revisit Narain conformal field theories ()from an algebraic perspective based on finite dimensional Lie algebras and representations , and show how the root and weight lattices can encode the momenta and subsequently the partition functions of Narain theories. In this framework, we construct a realisation of the Zamolodchikov metric of the moduli space in terms of Lie algebraic data, namely, the Cartan matrix and its inverse . Properties regarding the ensemble averaging of these CFTs and their holographic dual are also derived. Additionally, we discuss possible generalisations to NCFTs having dis‐symmetric central charges with , and highlight further features of the partition function .

ABSTRACT In the Euclidean view, one must first require that positivity not be violated, and from this modest demand, together with locality, a great deal follows: starting from a reflection‐positive lattice formulation of pure Yang–Mills theory we obtain a transfer operator with a uniform gap, while large Wilson loops already show an area law by means of convergent character (polymer) expansions; a finite‐range, gauge‐covariant multiscale analysis then carries these features from one scale to the next with interlaced inequalities whose small defects can be summed, so that exponential clustering and a strictly positive string tension endure in the continuum; the Osterwalder–Schrader reconstruction turns these Euclidean facts into a Minkowski theory with a self‐adjoint Hamiltonian, the spectral gap lying above the vacuum and the linear potential for static charges appearing, which gives a concrete picture of confinement; the construction depends on no special regulator, for a single‐scale Lipschitz control and a telescoping argument bind all admissible reflection‐positive slicings into a unique limiting measure and thus secure universality; moreover, the same framework admits entry from weak coupling, so that the continuum reached from strong coupling meets the one approached along an asymptotically free trajectory, yielding one and the same theory; in my view this is how mathematical clarity and physical insight cooperate: positivity, locality, and renormalization working together so that the mass gap and confinement are not marvels to be assumed, but natural properties of the non‐Abelian vacuum.

ABSTRACT This work presents a systematic evaluation of near‐zero‐error encoding strategies for coherent‐state quantum communication, comparing homodyne and threshold detection across alphabet sizes . Simulations were performed for coherent amplitudes and channel transmittance values , enabling a detailed characterization of bit‐error rate (BER), optimal operating points, and information‐theoretic performance. Threshold detection was found to tend to saturate near for all , consistent with its limited ability to discriminate low‐energy coherent states. In contrast, homodyne detection exhibited exponential‐like BER suppression, reaching values below for , at and . Error exponent fits further revealed strong scaling behavior, with slopes increasing from 0.8 at to 45 at , suggesting the benefits of redundancy‐assisted encoding. Optimal amplitude extraction showed that within the tested grid minimized BER across all loss conditions examined. Capacity proxy evaluation demonstrated that homodyne in these simulations approaches the theoretical limit , achieving bits, while threshold detection remained substantially below capacity. Additional metrics, including and relative BER gain, indicated improvements of up to 2.5 bits and over two orders of magnitude, respectively. All simulations were implemented in Python using PennyLane–Strawberry Fields interfaces, executed entirely on classical hardware to support transparency and reproducibility.

ABSTRACT We construct 4D de Sitter space as an excited state, rather than as a vacuum configuration, in type IIB, heterotic , and heterotic string theories. This framework provides a mechanism to evade vacuum‐based no‐go theorems for de Sitter solutions in string theory. Starting from a generic M‐theory configuration, we obtain de Sitter isometry in the dual string theories through appropriate dynamical duality sequences in the late‐time limit. The excited state, identified as a Glauber–Sudarshan state, is constructed as the expectation value of the metric operator in M‐theory using path‐integral techniques. We further analyze the conditions required for the existence of a well‐defined effective field theory description and show that these conditions are equivalent to the null energy condition for a 4D Friedmann‐Lemaitre‐Robertson‐Walker cosmology. Finally, we investigate constraints arising from axionic cosmology, and demonstrate how the time‐dependent solutions are modified when experimental bounds on the axionic coupling constant are taken into account. This article serves as a computational companion to Sections 3 and 4 of the paper arXiv:2511.03798 [hep‐th], where we present the detailed intermediate steps underlying the analysis in those sections.

ABSTRACT This paper undertakes a conceptual re‐examination of several foundational elements of cosmology through the lens of spacetime symmetries. A new derivation of the Friedmann–Lemaître–Robertson–Walker metric is obtained by a careful conceptual examination of rotations and translations on generic manifolds, followed by solving the rotational and translational Killing equations, yielding both the metric and its translational generators for without any further assumptions. We then analyze how continuous symmetries are inherited by the Einstein tensor and the Hilbert energy–momentum tensor, proving two general propositions. Furthermore, we use the Maxwell and Kalb–Ramond fields to show that a homogeneous and isotropic energy–momentum tensor, in general, does not give rise to field configurations which share these symmetries. In particular, the Kalb–Ramond field we derive is significantly more general than what is usually encountered in the cosmological context. Finally, we provide a rigorous but accessible, elementary, and transparent derivation of the scalar–vector–tensor decomposition from the linearized Einstein equations. Together, these results highlight the value of multiple complementary formulations of the same cosmological physics.

ABSTRACT We develop a thermodynamically consistent nonperturbative framework for equilibrium criticality in QCD matter by unifying Dyson–Schwinger quark propagation, functional renormalization‐group (FRG) evolution of the effective action, and Polyakov–Nambu–Jona–Lasinio (PNJL) thermodynamics for the coupled chiral and deconfinement order parameters. A holographic Maxwell–Chern–Simons sector supplies the topological response, and its topological susceptibility is fed into the FRG flow of the determinantal ('t Hooft) interaction to encode the evolution of the axial anomaly across the phase diagram. At , the construction is anchored to continuum‐extrapolated lattice thermodynamics and conserved‐charge susceptibilities through a lattice‐calibrated Polyakov sector, while exact thermodynamic identities are enforced by evaluating all derivatives at the stationary solution of the grand potential at each RG scale. Solving the coupled DSE, FRG, and holographic system yields, within this framework and at the present level of approximation, an equilibrium critical end point (CEP) at to and together with an internally quantified sensitivity to regulator, Polyakov‐sector, and holographic‐normalization variations. The critical region is organized by a nonperturbative mapping to universal 3D Ising scaling variables with anomalous‐dimension effects absorbed into nonuniversal metric factors, leading to equilibrium predictions for the hierarchy, nonmonotonicity, and sign structure of higher‐order net‐baryon cumulant ratios along the smooth freeze‐out trajectories, as well as equilibrium softening of the speed of sound. Comparisons to RHIC beam energy scan fluctuation measurements are presented as qualitative consistency checks on correlated equilibrium trends and sign patterns, because finite size and lifetime, critical slowing down, baryon number conservation, acceptance and efficiency corrections, the net‐proton to net‐baryon conversion, and baryon‐transport dynamics can round or reshape cumulants in the experimental system. The results, therefore, provide a unified equilibrium baseline and a set of controlled inputs for finite‐size scaling and dynamical embeddings of heavy‐ion data.